Consider the functions $f(x) = \frac{1}{x-a}$ and $g(x) = \sqrt{x}$, where $a$ is a real number. Analyse the conditions on $a$ for which the composite function $f(g(x))$ is defined. Furthermore, determine the domain of $f(g(x))$ for each valid condition on $a$.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 5 marks, testing your understanding of Composition of Functions. It falls under Algebra, number and structure in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers algebra of functions, inverse functions, and solutions of equations and systems of equations.
composition of functions, where $f$ composite $g, f \circ g$, is defined by $(f \circ g)(x)=f(g(x))$ given $r_{g} \subseteq d_{f}$
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